[music-dsp] zero delay feedback using sample prediction

[eli+ at gs211.sp.cs.cmu.edu]

Theo wrote:
> Yes we are trying to predict the filter output, not the input.
> But compared to the situation when the input is a complex natural sound
> (for example a chaotic attack transient)  the task of predicting the output
> is
> much simpler when the input is a simple waveform of constant amplitude.

Easier, yeah.  I just wanted to highlight that the predictor is not
just based on looking at the past values of y and doing any kind of
spline-based psychoacoustic whatever.  The predictor depends on f, and
has to pay attention to x.  After all, the ideal predictor would be
    y(t) = (Y (f x(t))) 
where Y is the fixed point combinator.  It might be better to call
this problem "guessing the fixed point" rather than predicting anything.

> >     y^(t) = g x(t-1) y(t-1)

    y^(t) = g x(t) y(t-1)
would have made more sense here.

> Point is how many iterations do you need before getting a "good enough"
> answer,
> I hoped that prediction could be cheaper.
> From the reaction on this treat it seems that the idea might work,
> but may not be economic.

Hard to say anything without talking about a particular function f.
In simple enough cases, you can get a closed form for the fixed point.
In general, my gut feeling is that predicting the fixed point will be
too hard to do well enough to be useful, but try it and see.

-- 
     Eli Brandt  |  eli+ at cs.cmu.edu  |  http://www.cs.cmu.edu/~eli/

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